Just believe in yourself. It's fine to be a lesbian, even though I'm straight. Things will work out, just tell your parents that it's okay to be lesbian. Tell them that one of our liberties is freedom of sexuality.

No, I don't think they hate you.. It's just that, they're not in your place so they probably don't get your point and they don't understand you. But don't worry, in the end, there will be acceptance and forgiveness. You just have to wait for it.

They do not hate you. They probably are clueless why you are a lesbian. They probably think that you’d be straight. But that’s fine. You should stay who you really are. And you will find that special girl.